National University of Science and Technology MISiS, Moscow, Russia:

K. V. Khalkechev, Professor, Doctor of Physico-Mathematical Sciences, h_kemal@mail.ru
R. K. Khalkechev, Associate Professor, Candidate of Physico-Mathematical Sciences

With a view to represent mathematically nonuniform elastic stress field in rock mass composed of blocks, the authos build a conceptual model in accordance with the general framework of the use of mathematics. Operating a classification of structural joints based on their scales, the model allows identifying rock blocks where stress field is definable. For such rock blocks, a set of mathematical models has been generated in the form of a system of integral equations describing deformation of rock blocks at the levels of structure, texture and rock mass. The analysis of this system of equations in the framework of the theory of pseudo-differential equations and the self-consistent field theory has yielded relations to calculate stress fields at all of the listed above levels. These relations, moreover, allow the rock mass stress field to be calculated at any degree of connection between the structural rock blocks. For instance, the computer-aided experiments on determination of stresses in grains of different minerals show that, given negligible friction over surfaces of joints, some grains undergo multiaxial stress; grains distributed across the entire volume of blocks feel tensile stresses oriented in perpendicular to external compressive stresses, at the same time, when friction is high and sliding over surfaces of joints is excluded, all grains experience triaxial stresses and only some grains outside such domains feel tensile stresses. The obtained knowledge on stress–strain state of a blockstructured rock mass enable geomechanical control, such that stability is ensured when required or caving is induced in designed areas of rocks mass when necessary. For example, in underground mining with room-and-pillar method, microscopic stress field is induced in rock pillars, which contributes to the stability of the pillars and results in an increase in production. On the other hand, with only microscopic nonuniform stress field generated in the face area, caving is possible at smaller energy inputs.

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11. Khalkechev K. V. Ierarkhiya sluchayno-fraktalnykh modeley razrusheniya konstruktsionnykh materialov (Hierarchy of the chance-fractal models of structural material destruction). Obozrenie prikladnoy i promyshlennoy matematiki = Review of applied and industrial mathematics. 2006. Vol. 13, No. 3. pp. 409–433.
12. Khalkechev R. K. Skeyling gazosoderzhashchikh porodnykh massivov (Scaling of gascon taining rock massifs). Izvestiya vysshikh uchebnykh zavedeniy. Severo-Kavkazskiy region. Tekhnicheskie nauki = University News. North-Caucasian Region. Technical Sciences Series. 2012. No. 2. pp. 102–104.
13. Khalkechev R. K. Stokhasticheskiy metod opredeleniya elementarnykh obemov kris tal li cheskikh i kompozitsionnykh geomaterialov (Stochastic method of definition of voluentary units of crystalline and composite geomaterials). Izvestiya Kabardino-Balkarskogo nauchnogo tsentra Rossiyskoy Akademii Nauk = News of the Kabardino-Balkarian Scientific Center of the Russian Academy of Sciences. 2012. No. 2. pp. 38–41.